Question

The equation h = 7 cos (pi/3 t) models the height h in centimeters after t seconds of a weight attached to the end of a spring that has been stretched and then released.

a. Solve the equation for t.
b. Find the times at which the weight is first at a height of 1 cm, of 3 cm, and of 5 cm above the rest position. Round your answers to the nearest hundredth.
c. Find the times at which the weight is at a height of 1 cm, of 3 cm, and of 5 cm below the rest position for the second time. Round your answers to the nearest hundredth.

Answer 1

I already have the answers to A & B, but i need some help with C. will you tell me if my answers are correct?


A: h=7cos(pi/3)t
h/7=cos(pi/3)t
arccos(h/7)=pi
t=3arccos(h/7)/pi
final answer: 3/pi cos^-1 (h/7)

B: h=1cm t=3arccos(1/7)/pi≈1.36 sec
h=3cm t=3arccos(3/7)/pi≈1.08 sec
h=5cm t=3arccos(5/7)/pi≈0.74 sec

Answer 2

is the term pi/3 or pi/3t?

Answer 3

it's \[\pi t/3\]

Answer 4

@DemolisionWolf